#### Vol. 4, No. 1, 2011

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editors’ Interests Scientific Advantages Submission Guidelines Submission Form Editorial Login Ethics Statement Contacts Author Index To Appear ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Other MSP Journals
Three-term commutator estimates and the regularity of $\half$-harmonic maps into spheres

### Francesca Da Lio and Tristan Rivière

Vol. 4 (2011), No. 1, 149–190
##### Abstract

We prove the regularity of weak $\frac{1}{2}$-harmonic maps from the real line into a sphere. A key step is the formulation of the $\frac{1}{2}$-harmonic map equation in the form of a nonlocal linear Schrödinger type equation with three-term commutators on the right-hand side. We then establish a sharp estimate for these three-term commutators.

##### Keywords
harmonic map, nonlinear elliptic PDE, regularity of solutions, commutator estimates
##### Mathematical Subject Classification 2000
Primary: 58E20, 35B65, 35J20, 35J60, 35S99